Question

I have a 2005 Chrysler 300 that will not shift out of park.

Yesterday the car was driving and shifting just fine. This morning when the car was started and I tried to put the car in reverse to back out of the garage, the gear would not go into reverse. It would not move from the park position.

Your problem is with the brake shift interlock system that prevents gear engagement when the brake is not pressed. Most likely, the problem is a bad brake switch that is located at the brake pedal arm under the driver's side dash. It is also possible that the solenoid that locks the gear shifter is malfunctioning. Most of the time a quick shot of WD40 to the solenoid will free up the pintel that locks the gear shift. You can access it by removing the gear shift cover plate. To be able to operate the car, there will be a small hole near the gear shifter that allows you to put a small screwdriver down it to free up the gear shifter. This allows you to get the car going until you can get it repaired.